Vibration characteristics of piezoelectric annular plates with annular metallization: An extended polynomial method

The vibration characteristics of axially polarized annular MEMS resonators with partial metal deposition have been investigated using an extended polynomial method (EPM). Differences in electrode distribution and electrical boundary conditions require the structure to be divided into two distinct regions. Wave propagation is modeled by expanding mechanical displacements and electrical potentials into appropriate polynomial series and incorporating window functions, while accounting for variations between the regions. The outcomes of the proposed method, which employs modal and harmonic analyses, are validated by comparing them to previous findings from the literature. The study examines the influence of the metal deposition rate on the radial extensional resonant frequencies (RFs) and antiresonant frequencies (AFs), dispersion curves, and electromechanical coupling coefficients (EMCCs). The results show that the dispersion curves shift to higher frequencies as the metal deposition rate decreases. Moreover, depending on the electrode distribution, the EMCC can increase by a factor of up to 8.85 compared to complete metallization (CM). These findings are further supported by detailed evaluations of impedance response patterns and field profiles. These analyses provide a comprehensive understanding of the mechanical and electrical behaviors of annular piezoelectric plates, allowing for the optimization of the design of annular piezoelectric MEMS resonators.